In data networks designed to receive, switch and transmit analog signals, digital devices are attached to a communication line via a modem that converts digital data to analog line signals and vice versa. The modem modulates data prior to sending them over such communication lines as a telephone wire, a CATV coaxial cable, an optical cable, or a wireless communication link. The basis for analog signal transmission is a continuous constant-frequency signal known as a carrier signal. For example, the carrier signal may be defined as v.sub.s.sup.' (t)=V.sub.s cos(2.pi.ft+.phi..sub.s), where f is the frequency, V.sub.s is the amplitude, and .phi..sub.s is the phase of the carrier signal. Modulation involves operation on one or more of the three characteristics of the carrier signal: amplitude, frequency or phase. Accordingly, three basic modulation techniques are used for transforming digital data into analog line signals: amplitude modulation, frequency-shift keying and phase modulation or phase-shift keying.
Digital data are represented by a finite number of values, each of which defines a digital symbol. Each symbol may be composed of one or more bits. Amplitude modulation enables a modem to transmit analog equivalents of digital symbols by varying the amplitude of the carrier signal. For example, if a symbol consists of two bits, the entire continuous range of the signal amplitudes is divided into four bands, each of which represents one of four possible symbols 00, 01, 10 or 11. For instance, for a signal in a range from -3 V to 3 V, amplitudes smaller than -2 V may represent 00, amplitudes between -2 V and 0 V may correspond to 01, amplitudes between 0 V and 2 V may represent 10, and amplitudes larger than 2 V may correspond to 11. Alternatively, such transformation may be carried out by pulse-amplitude modulation that uses a pulse carrier.
Frequency-shift keying may use different frequencies of the carrier signal to represent binary 1 and binary 0. This technique is suitable for low-speed devices.
In phase modulation, the carrier signal is shifted a certain number of degrees in response to the digital pattern coming from a digital device. For example, to represent two-bit symbols 00, 01, 10 or 11, four phase values of the carrier signal are required. For instance, a phase value between 0 and .pi./2 may correspond to 00, a phase value between .pi./2 and .pi. may represent 01, etc.
Amplitude and phase modulations of a carrier signal may be combined to form a line signal with amplitude and phase representing digital data to be transmitted. Each symbol of the digital data may be defined as a vector with a certain length represented by the amplitude of the line signal, and a certain angle or phase with respect to a reference, for example, the horizontal axis. For instance, in each 4-bit digital symbol, two bits may be represented by four different values of amplitude, and two bits may be represented by four different values of phase.
Various demodulation techniques have been developed for modems that convert digital data into modulated analog signals at a transmitting side and recover the digital data from the analog signals at a receiving side. These techniques are built either entirely on digital circuitry or entirely on analog circuitry. However, digital demodulators are slow and may be used only for low-speed applications, such as voice-band modems. Although analog demodulators are much faster than the digital systems, their reliability is poor.
Thus, it would be desirable to provide a novel demodulation system for recovery digital data from analog line signals, which would be faster than the digital systems and more reliable than the analog systems.
Also, it would be desirable to provide a novel system for demodulating amplitude and phase modulated line signals representing digital data.